/* ----------------------------------------------------------------------
* Copyright (C) 2010 ARM Limited. All rights reserved.
*
* $Date:        15. February 2012
* $Revision: 	V1.1.0
*
* Project: 	    CMSIS DSP Library
* Title:	    arm_lms_f32.c
*
* Description:	Processing function for the floating-point LMS filter.
*
* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0
*
* Version 1.1.0 2012/02/15
*    Updated with more optimizations, bug fixes and minor API changes.
*
* Version 1.0.10 2011/7/15
*    Big Endian support added and Merged M0 and M3/M4 Source code.
*
* Version 1.0.3 2010/11/29
*    Re-organized the CMSIS folders and updated documentation.
*
* Version 1.0.2 2010/11/11
*    Documentation updated.
*
* Version 1.0.1 2010/10/05
*    Production release and review comments incorporated.
*
* Version 1.0.0 2010/09/20
*    Production release and review comments incorporated
*
* Version 0.0.7  2010/06/10
*    Misra-C changes done
* -------------------------------------------------------------------- */

#include "arm_math.h"

/**
 * @ingroup groupFilters
 */

/**
 * @defgroup LMS Least Mean Square (LMS) Filters
 *
 * LMS filters are a class of adaptive filters that are able to "learn" an unknown transfer functions.
 * LMS filters use a gradient descent method in which the filter coefficients are updated based on the instantaneous error signal.
 * Adaptive filters are often used in communication systems, equalizers, and noise removal.
 * The CMSIS DSP Library contains LMS filter functions that operate on Q15, Q31, and floating-point data types.
 * The library also contains normalized LMS filters in which the filter coefficient adaptation is indepedent of the level of the input signal.
 *
 * An LMS filter consists of two components as shown below.
 * The first component is a standard transversal or FIR filter.
 * The second component is a coefficient update mechanism.
 * The LMS filter has two input signals.
 * The "input" feeds the FIR filter while the "reference input" corresponds to the desired output of the FIR filter.
 * That is, the FIR filter coefficients are updated so that the output of the FIR filter matches the reference input.
 * The filter coefficient update mechanism is based on the difference between the FIR filter output and the reference input.
 * This "error signal" tends towards zero as the filter adapts.
 * The LMS processing functions accept the input and reference input signals and generate the filter output and error signal.
 * \image html LMS.gif "Internal structure of the Least Mean Square filter"
 *
 * The functions operate on blocks of data and each call to the function processes
 * <code>blockSize</code> samples through the filter.
 * <code>pSrc</code> points to input signal, <code>pRef</code> points to reference signal,
 * <code>pOut</code> points to output signal and <code>pErr</code> points to error signal.
 * All arrays contain <code>blockSize</code> values.
 *
 * The functions operate on a block-by-block basis.
 * Internally, the filter coefficients <code>b[n]</code> are updated on a sample-by-sample basis.
 * The convergence of the LMS filter is slower compared to the normalized LMS algorithm.
 *
 * \par Algorithm:
 * The output signal <code>y[n]</code> is computed by a standard FIR filter:
 * <pre>
 *     y[n] = b[0] * x[n] + b[1] * x[n-1] + b[2] * x[n-2] + ...+ b[numTaps-1] * x[n-numTaps+1]
 * </pre>
 *
 * \par
 * The error signal equals the difference between the reference signal <code>d[n]</code> and the filter output:
 * <pre>
 *     e[n] = d[n] - y[n].
 * </pre>
 *
 * \par
 * After each sample of the error signal is computed, the filter coefficients <code>b[k]</code> are updated on a sample-by-sample basis:
 * <pre>
 *     b[k] = b[k] + e[n] * mu * x[n-k],  for k=0, 1, ..., numTaps-1
 * </pre>
 * where <code>mu</code> is the step size and controls the rate of coefficient convergence.
 *\par
 * In the APIs, <code>pCoeffs</code> points to a coefficient array of size <code>numTaps</code>.
 * Coefficients are stored in time reversed order.
 * \par
 * <pre>
 *    {b[numTaps-1], b[numTaps-2], b[N-2], ..., b[1], b[0]}
 * </pre>
 * \par
 * <code>pState</code> points to a state array of size <code>numTaps + blockSize - 1</code>.
 * Samples in the state buffer are stored in the order:
 * \par
 * <pre>
 *    {x[n-numTaps+1], x[n-numTaps], x[n-numTaps-1], x[n-numTaps-2]....x[0], x[1], ..., x[blockSize-1]}
 * </pre>
 * \par
 * Note that the length of the state buffer exceeds the length of the coefficient array by <code>blockSize-1</code> samples.
 * The increased state buffer length allows circular addressing, which is traditionally used in FIR filters,
 * to be avoided and yields a significant speed improvement.
 * The state variables are updated after each block of data is processed.
 * \par Instance Structure
 * The coefficients and state variables for a filter are stored together in an instance data structure.
 * A separate instance structure must be defined for each filter and
 * coefficient and state arrays cannot be shared among instances.
 * There are separate instance structure declarations for each of the 3 supported data types.
 *
 * \par Initialization Functions
 * There is also an associated initialization function for each data type.
 * The initialization function performs the following operations:
 * - Sets the values of the internal structure fields.
 * - Zeros out the values in the state buffer.
 * \par
 * Use of the initialization function is optional.
 * However, if the initialization function is used, then the instance structure cannot be placed into a const data section.
 * To place an instance structure into a const data section, the instance structure must be manually initialized.
 * Set the values in the state buffer to zeros before static initialization.
 * The code below statically initializes each of the 3 different data type filter instance structures
 * <pre>
 *    arm_lms_instance_f32 S = {numTaps, pState, pCoeffs, mu};
 *    arm_lms_instance_q31 S = {numTaps, pState, pCoeffs, mu, postShift};
 *    arm_lms_instance_q15 S = {numTaps, pState, pCoeffs, mu, postShift};
 * </pre>
 * where <code>numTaps</code> is the number of filter coefficients in the filter; <code>pState</code> is the address of the state buffer;
 * <code>pCoeffs</code> is the address of the coefficient buffer; <code>mu</code> is the step size parameter; and <code>postShift</code> is the shift applied to coefficients.
 *
 * \par Fixed-Point Behavior:
 * Care must be taken when using the Q15 and Q31 versions of the LMS filter.
 * The following issues must be considered:
 * - Scaling of coefficients
 * - Overflow and saturation
 *
 * \par Scaling of Coefficients:
 * Filter coefficients are represented as fractional values and
 * coefficients are restricted to lie in the range <code>[-1 +1)</code>.
 * The fixed-point functions have an additional scaling parameter <code>postShift</code>.
 * At the output of the filter's accumulator is a shift register which shifts the result by <code>postShift</code> bits.
 * This essentially scales the filter coefficients by <code>2^postShift</code> and
 * allows the filter coefficients to exceed the range <code>[+1 -1)</code>.
 * The value of <code>postShift</code> is set by the user based on the expected gain through the system being modeled.
 *
 * \par Overflow and Saturation:
 * Overflow and saturation behavior of the fixed-point Q15 and Q31 versions are
 * described separately as part of the function specific documentation below.
 */

/**
 * @addtogroup LMS
 * @{
 */

/**
 * @details
 * This function operates on floating-point data types.
 *
 * @brief Processing function for floating-point LMS filter.
 * @param[in]  *S points to an instance of the floating-point LMS filter structure.
 * @param[in]  *pSrc points to the block of input data.
 * @param[in]  *pRef points to the block of reference data.
 * @param[out] *pOut points to the block of output data.
 * @param[out] *pErr points to the block of error data.
 * @param[in]  blockSize number of samples to process.
 * @return     none.
 */

void arm_lms_f32(
    const arm_lms_instance_f32* S,
    float32_t* pSrc,
    float32_t* pRef,
    float32_t* pOut,
    float32_t* pErr,
    uint32_t blockSize)
{
	float32_t* pState = S->pState;                 /* State pointer */
	float32_t* pCoeffs = S->pCoeffs;               /* Coefficient pointer */
	float32_t* pStateCurnt;                        /* Points to the current sample of the state */
	float32_t* px, *pb;                            /* Temporary pointers for state and coefficient buffers */
	float32_t mu = S->mu;                          /* Adaptive factor */
	uint32_t numTaps = S->numTaps;                 /* Number of filter coefficients in the filter */
	uint32_t tapCnt, blkCnt;                       /* Loop counters */
	float32_t sum, e, d;                           /* accumulator, error, reference data sample */
	float32_t w = 0.0f;                            /* weight factor */

	e = 0.0f;
	d = 0.0f;

	/* S->pState points to state array which contains previous frame (numTaps - 1) samples */
	/* pStateCurnt points to the location where the new input data should be written */
	pStateCurnt = &(S->pState[(numTaps - 1u)]);

	blkCnt = blockSize;


#ifndef ARM_MATH_CM0

	/* Run the below code for Cortex-M4 and Cortex-M3 */

	while(blkCnt > 0u) {
		/* Copy the new input sample into the state buffer */
		*pStateCurnt++ = *pSrc++;

		/* Initialize pState pointer */
		px = pState;

		/* Initialize coeff pointer */
		pb = (pCoeffs);

		/* Set the accumulator to zero */
		sum = 0.0f;

		/* Loop unrolling.  Process 4 taps at a time. */
		tapCnt = numTaps >> 2;

		while(tapCnt > 0u) {
			/* Perform the multiply-accumulate */
			sum += (*px++) * (*pb++);
			sum += (*px++) * (*pb++);
			sum += (*px++) * (*pb++);
			sum += (*px++) * (*pb++);

			/* Decrement the loop counter */
			tapCnt--;
		}

		/* If the filter length is not a multiple of 4, compute the remaining filter taps */
		tapCnt = numTaps % 0x4u;

		while(tapCnt > 0u) {
			/* Perform the multiply-accumulate */
			sum += (*px++) * (*pb++);

			/* Decrement the loop counter */
			tapCnt--;
		}

		/* The result in the accumulator, store in the destination buffer. */
		*pOut++ = sum;

		/* Compute and store error */
		d = (float32_t)(*pRef++);
		e = d - sum;
		*pErr++ = e;

		/* Calculation of Weighting factor for the updating filter coefficients */
		w = e * mu;

		/* Initialize pState pointer */
		px = pState;

		/* Initialize coeff pointer */
		pb = (pCoeffs);

		/* Loop unrolling.  Process 4 taps at a time. */
		tapCnt = numTaps >> 2;

		/* Update filter coefficients */
		while(tapCnt > 0u) {
			/* Perform the multiply-accumulate */
			*pb = *pb + (w * (*px++));
			pb++;

			*pb = *pb + (w * (*px++));
			pb++;

			*pb = *pb + (w * (*px++));
			pb++;

			*pb = *pb + (w * (*px++));
			pb++;

			/* Decrement the loop counter */
			tapCnt--;
		}

		/* If the filter length is not a multiple of 4, compute the remaining filter taps */
		tapCnt = numTaps % 0x4u;

		while(tapCnt > 0u) {
			/* Perform the multiply-accumulate */
			*pb = *pb + (w * (*px++));
			pb++;

			/* Decrement the loop counter */
			tapCnt--;
		}

		/* Advance state pointer by 1 for the next sample */
		pState = pState + 1;

		/* Decrement the loop counter */
		blkCnt--;
	}


	/* Processing is complete. Now copy the last numTaps - 1 samples to the
	   satrt of the state buffer. This prepares the state buffer for the
	   next function call. */

	/* Points to the start of the pState buffer */
	pStateCurnt = S->pState;

	/* Loop unrolling for (numTaps - 1u) samples copy */
	tapCnt = (numTaps - 1u) >> 2u;

	/* copy data */
	while(tapCnt > 0u) {
		*pStateCurnt++ = *pState++;
		*pStateCurnt++ = *pState++;
		*pStateCurnt++ = *pState++;
		*pStateCurnt++ = *pState++;

		/* Decrement the loop counter */
		tapCnt--;
	}

	/* Calculate remaining number of copies */
	tapCnt = (numTaps - 1u) % 0x4u;

	/* Copy the remaining q31_t data */
	while(tapCnt > 0u) {
		*pStateCurnt++ = *pState++;

		/* Decrement the loop counter */
		tapCnt--;
	}

#else

	/* Run the below code for Cortex-M0 */

	while(blkCnt > 0u) {
		/* Copy the new input sample into the state buffer */
		*pStateCurnt++ = *pSrc++;

		/* Initialize pState pointer */
		px = pState;

		/* Initialize pCoeffs pointer */
		pb = pCoeffs;

		/* Set the accumulator to zero */
		sum = 0.0f;

		/* Loop over numTaps number of values */
		tapCnt = numTaps;

		while(tapCnt > 0u) {
			/* Perform the multiply-accumulate */
			sum += (*px++) * (*pb++);

			/* Decrement the loop counter */
			tapCnt--;
		}

		/* The result is stored in the destination buffer. */
		*pOut++ = sum;

		/* Compute and store error */
		d = (float32_t)(*pRef++);
		e = d - sum;
		*pErr++ = e;

		/* Weighting factor for the LMS version */
		w = e * mu;

		/* Initialize pState pointer */
		px = pState;

		/* Initialize pCoeffs pointer */
		pb = pCoeffs;

		/* Loop over numTaps number of values */
		tapCnt = numTaps;

		while(tapCnt > 0u) {
			/* Perform the multiply-accumulate */
			*pb = *pb + (w * (*px++));
			pb++;

			/* Decrement the loop counter */
			tapCnt--;
		}

		/* Advance state pointer by 1 for the next sample */
		pState = pState + 1;

		/* Decrement the loop counter */
		blkCnt--;
	}


	/* Processing is complete. Now copy the last numTaps - 1 samples to the
	 * start of the state buffer. This prepares the state buffer for the
	 * next function call. */

	/* Points to the start of the pState buffer */
	pStateCurnt = S->pState;

	/*  Copy (numTaps - 1u) samples  */
	tapCnt = (numTaps - 1u);

	/* Copy the data */
	while(tapCnt > 0u) {
		*pStateCurnt++ = *pState++;

		/* Decrement the loop counter */
		tapCnt--;
	}

#endif /*   #ifndef ARM_MATH_CM0 */

}

/**
   * @} end of LMS group
   */
